The force F is inclined to the x axis at 60 degrees.
To find the the horizontal and vertical components.
Le the horizontal line be x axis and the vertical line be y axis.
Then resolving the force 10 lb along the horizontal line , we get:
Horizontal component = 10lb cos60 deg = 10*(1/2) = 5 lb along x axis.
The vertical component of 10 lb = 10lb sin60 = 10lb sin 60 = 10*(sqrt3)/2 = 5 sqrt3 lb = 8.66lb approx. along y axis.
Therefore the horizontal and the vertical components of the 10 lb force are 5lb and 8.66lb respectively.
Since the force is a vector, it's components are the projections of the resultant force of 10 lb. on x and y axis.
The vector of force is making a 60 degrees angle to x axis.
To compute it's x axis component, we'll apply cosine function.
cos 60 = Fx/F
Fx = F*cos 60
Fx = 10*(1/2)
Fx = 5 lb.
To compute the component on y axis, we'll apply sine function:
sin 60 = Fy/F
Fy = F*sin 60
Fy = 10*(sqrt3/2)
Fy = 5*sqrt3
Fy = 8.66 lb.